We study a problem raised by Abdenur et. al. [3] that asks,
for any chain transitive set $\Lambda$ of a generic diffeomorphism
$f$, whether the set $I(\Lambda)$ of indices of hyperbolic periodic
orbits that approach $\Lambda$ in the Hausdorff metric must be an
"interval", i.e., whether $\alpha\in I(\Lambda)$ and $\beta\in
I(\Lambda)$, $\alpha